1-At which stage a Sign Off can happen ? when is it signed in a predictive and in an adaptive life cycle ?Is it in the beginning or middle or at end of the solution?

The stage of sign-off is depended on the Business Analysis Plan. Yes, project Lifecycle influences the Business Analysis planning. In adaptive, it is less formal and may be done for each iteration.

Sign-off depend on the release decisions as well. The format and frequency of sign-off depends on project to project and details are available in the Business Analysis plan.

2-if evaluation is done at the end and the solution has been deployed then we do not need a Sign off ..please correct me if i am wrong .

It is not correct. Solution is deployed and evaluated for the benefits and agreement is needed that solution is delivered as per the expectations. For the agreement, sign off is needed. It may be verbal for simple projects or it may be complex process for large projects.